CN114462124A - Method for establishing and numerically simulating concrete three-dimensional multiphase mesoscopic model - Google Patents

Method for establishing and numerically simulating concrete three-dimensional multiphase mesoscopic model Download PDF

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CN114462124A
CN114462124A CN202210055162.XA CN202210055162A CN114462124A CN 114462124 A CN114462124 A CN 114462124A CN 202210055162 A CN202210055162 A CN 202210055162A CN 114462124 A CN114462124 A CN 114462124A
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郭小明
张维伦
胡道前
吴佰建
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Abstract

The invention relates to a method for establishing a concrete three-dimensional multiphase mesoscopic model and simulating a numerical value, which comprises the steps of firstly establishing a concrete three-dimensional random aggregate model, expanding an interface transition zone layer in a geometric model, and setting an inner grid transition surface and an outer grid transition surface to effectively reduce the number of units; on the basis, considering the non-uniformity of the interface transition area, and establishing a concrete three-dimensional multi-phase mesoscopic model; defining the tension plasticity damage constitutive relation of the concrete sample material; the displacement loading method is used for carrying out numerical simulation on the three-dimensional failure damage process of the concrete sample, simulation analysis is carried out on the damage and fracture condition inside the concrete, and the model established based on the application can show the damage evolution process of the concrete as a three-dimensional space structure more clearly.

Description

Method for establishing and numerically simulating concrete three-dimensional multiphase mesoscopic model
Technical Field
The invention relates to a method for establishing a concrete three-dimensional multiphase mesoscopic model and simulating a numerical value, belonging to the field of numerical simulation of concrete materials.
Background
In recent years, the urbanization process of China is continuously promoted, major infrastructure construction and engineering construction are in a high-speed development stage, large-scale engineering such as concrete dams, nuclear power plant concrete protective housings, high-rise buildings, high-speed railways, sea-crossing bridges and the like are closely connected with concrete materials, and the construction of modern engineering also puts higher requirements on the performance of the concrete materials. As one of the most widely used building materials at present, the safety and reliability of concrete directly affect the safety of building structures.
The heterogeneity of concrete itself and its complex internal structure make its failure mechanism very complex. According to different research focuses, students establish various concrete mesoscopic models. The multiphase mesoscopic model considers the heterogeneity inside the concrete and different mechanical parameters of each phase, so that the model has superiority in the simulation of the failure and damage problem of the concrete.
Because the modeling and calculation processes of the concrete two-dimensional mesoscopic model are relatively simple, early research is mostly concentrated on a two-dimensional layer, but in actual engineering, the method can be simplified into a three-dimensional problem of a plane stress problem (such as a thin plate) and a plane strain problem (such as a gravity dam), and a plurality of problems are difficult to be analyzed by being simplified into a two-dimensional problem.
Under the microscopic scale, the interface transition area is an important component of the concrete which is not negligible, and the interface transition area is generally simplified to different degrees in the three-dimensional model due to the consideration of calculated amount, so that the fine mesh generation is less. In the three-dimensional microscopic analysis, due to the limitation of computer capability, the problems of excessive simplification steps, unreasonable analysis process and the like inevitably exist, so that the analysis result of the three-dimensional model is not ideal. In order to facilitate the establishment of the model, more three-dimensional models simplify the shape of the aggregate into a spherical shape, but the simplification is more than ideal; in part of three-dimensional microscopic researches, the concrete is only considered as a two-phase material, and the effect of an interface transition area is neglected; most studies do not take into account the non-uniformity of the interfacial transition zone, but treat the interfacial transition zone outside different aggregates as a material of the same material properties, which inevitably affects the calculation results. The interface transition zone is a weak link of a concrete material, and the consideration of the interface transition zone is indispensable in mesoscopic analysis, so that the optimization of the interface transition zone model in a three-dimensional mesoscopic model is also one of important aspects of current research.
Disclosure of Invention
The invention provides a method for establishing a concrete three-dimensional multiphase mesoscopic model and simulating a numerical value, which introduces the method for establishing the concrete three-dimensional multiphase mesoscopic model and simulating the numerical value, wherein the mesoscopic model adopts a three-dimensional entity unit and considers the inconsistency of an interface transition region.
The technical scheme adopted by the invention for solving the technical problems is as follows:
a method for building and numerically simulating a three-dimensional multi-phase microscopic model of concrete specifically comprises the following steps:
step S1: establishing a concrete three-dimensional random aggregate model, wherein the concrete three-dimensional random aggregate model comprises a three-dimensional spherical aggregate model, a three-dimensional ellipsoid aggregate model and a three-dimensional random convex polyhedron aggregate model;
step S2: defining aggregate units based on the concrete three-dimensional random aggregate model established in the step S1, defining mortar units according to the size of the concrete test piece, and establishing a non-uniform concrete three-dimensional multi-phase mesoscopic model in the interface transition region;
step S3: setting an inner grid transition surface and an outer grid transition surface for the non-uniform concrete three-dimensional multi-phase mesoscopic model in the interface transition area;
step S4: based on the model obtained in the step S3, carrying out numerical simulation on the three-dimensional failure and damage process of the concrete test piece by using a displacement loading method;
as a further preferable aspect of the present invention, in step S1, the step of building a concrete three-dimensional random aggregate model specifically includes:
step S11: determining the number of the aggregates in each particle size range, and obtaining the percentage of the aggregates in each particle size range in the total volume of the aggregates by adopting a Fuller grading formula
Figure BDA0003476179310000021
In the formula (1), D0Is the diameter of the sieve hole, DmaxMaximum aggregate particle size, P, to pass through the screenc(D<D0) To pass through a diameter D0The aggregate cumulative volume percentage of the sieve pores is the percentage of the aggregate in the total volume in the particle size range;
substituting the percentage of the aggregate in the total volume in the obtained particle size range into a formula (2) to determine the number of the aggregates in each particle size range, wherein the formula (2) is
Figure BDA0003476179310000022
In the formula (2), DiThe aggregate in this particle size range represents the particle size, V is the total volume of the aggregate, PciThe volume of the aggregate accounts for the percentage of the total volume of the aggregate in the particle size range;
step S12: according to the Monte Carlo principle, randomly generating parameters of the aggregate in each particle size range, wherein the parameters comprise the position and the size parameters of the aggregate;
step S13: carrying out phase separation judgment on the aggregates by using the obtained aggregate parameters in each particle size range, namely carrying out phase separation judgment on spherical aggregates, ellipsoidal aggregates and random convex polyhedral aggregates;
step S14: embedding the Python program of the judgment result into ABAQUS to generate a three-dimensional random aggregate geometric model;
as a further preferred aspect of the present invention, in step S13, the phase separation determination of the aggregate mainly includes a method for determining the validity of a spherical aggregate, a quadratic matrix of a spatial ellipsoid, and a method for determining the validity of an ellipsoid aggregate;
the effectiveness judgment method of the spherical aggregate comprises the following steps: setting spherical aggregate Ai(xci,yci,zci) Spherical aggregate A0(xc0,yc0,zc0) Spherical aggregate AiSpherical aggregate A0Respectively is ri、r0Then the judgment equation is
Figure BDA0003476179310000031
Then, let the coordinates of the left lower corner point and the right upper corner point of the bounding cuboid be (x)L,yL,zL) And (x)U,yU,zU) The spherical center of each spherical aggregate is AiThe coordinates of the sphere center are (x)ci,yci,zci) Radius riThen spherical aggregate AiThe decision equation for separation from the boundary is:
Figure BDA0003476179310000032
spherical aggregate A0Is spherical aggregate AiBased on the random convex polyhedral aggregate A generated by adopting an inscription method0Each vertex position of the spherical aggregate A is random and is connected with the spherical aggregate AiOn the sphere, the coordinates of each vertex of the random convex polyhedron are expressed as
Figure BDA0003476179310000033
In the formula (4), the spherical aggregate A0Has a sphere center coordinate of (x)c0,yc0,zc0) Radius r0Let the coordinates start on the y-axis and be positive clockwise, αiIs an angle offset from the z-axis, positive in the clockwise direction, βiThe angle of rotation around the center of the sphere in the xOy plane;
then, similarly, let the coordinates of the left lower corner point and the right upper corner point of the bounding cuboid be (x) respectivelyL,yL,zL) And (x)U,yU,zU) Then random convex polyhedral aggregate A0The decision equation for separation from the boundary is:
Figure BDA0003476179310000034
the validity determination method of the ellipsoid aggregate comprises the following steps: let the quadratic forms of ellipsoid A and ellipsoid B be X respectivelyTAX is 0 and XTBX is 0, then the generalized characteristic polynomials of ellipsoid a and ellipsoid B are
f(λ)＝det(λA+B)，
If the equation f (λ) is 0, there are two different positive roots, then ellipsoid a is separated from ellipsoid B; ellipsoid A intersects ellipsoid B in other cases;
then, the method for determining the separation of the ellipsoidal aggregate from the boundary is as follows: the equations of the ellipsoid and the plane are combined to obtain a matrix equation
Figure BDA0003476179310000035
In the formula (6), the reaction mixture is,
Figure BDA0003476179310000036
is a three-order symmetrical square matrix,
order matrix
Figure BDA0003476179310000041
If matrices A and B satisfy the condition | A +>0 and (a)11+a22)|B|<0, the ellipsoid is intersected with the plane, otherwise, the ellipsoid is separated from the plane;
as a further preferable aspect of the present invention, the specific steps of establishing the three-dimensional multiphase mesoscopic model of the inconsistent concrete in the interface transition region in step S2 are as follows:
step S21: defining a tension plasticity damage constitutive relation and determining material parameters, wherein the tension plasticity damage constitutive relation formula is as follows
Figure BDA0003476179310000042
In formula (7), σtuIs the peak stress of the material, GfTo fracture energy, uckIs a cracking displacement;
step S22: establishing a three-dimensional multi-phase mesoscopic model of the non-uniform concrete in the interface transition region, wherein the three-dimensional multi-phase mesoscopic model comprises the linear proportional relation between the thickness of the interface transition region and the particle size of aggregate, and the exponential function relation between the strength of the interface transition region and the thickness of the interface transition region, and the relation between the strength of the interface transition region and the thickness of the interface transition region is
ξ＝ebδ-c+d (8)
In the formula (8), xi is the ratio of the strength of the interface transition area to the strength of the mortar, delta is the thickness of the interface transition area, c and d are parameters of an exponential function, and the two-point coordinate (delta)min,ξmax) And (delta)max,ξmin) Substituting the expression to obtain;
step S23: determining material parameters of the concrete test piece based on the formula (8), substituting the determined mortar strength, the strength of the interface transition zone and the fracture energy into the formula (7), determining the plastic damage parameters of the mortar and the interface transition zone, and generating sigma by using Python script programmingt-uckAnd dt-uckA table function;
step S24: wrapping an interface transition area in a thickness area outside the aggregate, and finishing the cutting and merging operation of an Assembly module in ABAQUS;
as a further preferred aspect of the present invention, in step S3, high-density grids are arranged in the interface transition area, the size of the seeds is equivalent to the thickness of the seeds, sparse grids are arranged in the aggregate units and the mortar units, and grid transition surfaces are arranged at the junctions of the interface transition area with the aggregate units and the mortar units, respectively, so that the high-density grids in the interface transition area are in smooth transition to the sparse grids in the aggregate units and the mortar units;
as a further preferred aspect of the present invention, the method for establishing the mesh transition surface is that a concentric surface concentric with the centroid of the aggregate and different in particle size is respectively established in the aggregate unit on the inner side of the interface transition zone and in the mortar unit on the outer side of the interface transition zone;
as a further preferred embodiment of the present invention, the step S4 includes the following steps:
step S41: applying boundary conditions to the non-uniform concrete three-dimensional multi-phase mesoscopic model of the interface transition area to be tested, and applying displacement load at a loading point;
step S42: setting a damage threshold, judging that the unit fails and breaks when the tensile damage value reaches the damage threshold, wherein the larger the damage value is, the more serious the material failure and damage is, and the damage threshold is 0.9;
step S43: storing the obtained damage value in a result information matrix, and processing elements in the result information matrix after calculation to finish the three-dimensional damage evolution process and the fracture form of the simulated concrete sample;
as a further preferred aspect of the present invention, when a three-dimensional multiphase mesoscopic model of concrete is subjected to test simulation, after a damage threshold is set, a damage cloud chart at the end of ABAQUS calculation is used to describe the failure damage form and damage fracture degree of a material;
and simultaneously, when the load is applied to the side boundary of the uniaxial tension test piece for analysis, the damage evolution process and the failure damage form of a plurality of sections of the concrete test piece are analyzed.
Through the technical scheme, compared with the prior art, the invention has the following beneficial effects:
1. according to the invention, a three-dimensional spherical aggregate model, a three-dimensional ellipsoid aggregate model and a three-dimensional random convex polyhedron aggregate model are established, and the separation judgment between the aggregates and the boundary and between the aggregates is carried out by a more accurate method, so that the time required by the aggregate separation judgment can be greatly reduced;
2. the non-uniformity of the interface transition region is considered in the concrete three-dimensional multi-phase mesoscopic model, namely the thickness and the strength of the interface transition region outside each aggregate change along with the change of the particle size of the aggregate, and the mechanical properties of the interface transition region are truly reflected;
3. according to the invention, the grid transition surfaces are respectively arranged in the aggregate units on the inner side of the interface transition area and the mortar units on the outer side of the interface transition area, so that the total amount of the units of the model is effectively reduced while the characteristics of the concrete three-dimensional multiphase mesoscopic model are fully embodied, and the calculation efficiency of the model is improved;
4. the method adopts a plurality of microscopic sections to analyze the three-dimensional failure damage process of the concrete sample, compares the damage cloud picture of the interface transition area inside the concrete sample with the macroscopic damage cloud picture outside the sample, and clearly shows the damage evolution process of the concrete sample as a three-dimensional space structure.
Drawings
The invention is further illustrated with reference to the following figures and examples.
Fig. 1 a-1 b are aggregate models provided by the present invention, wherein fig. 1a is a three-dimensional ellipsoid aggregate model, and fig. 1b is a three-dimensional random convex polyhedron aggregate model;
FIG. 2 is a plot of interfacial transition zone strength versus interfacial transition zone thickness;
FIGS. 3 a-3 b are boundary transition zones for different aggregates, wherein FIG. 3a is a boundary transition zone for an ellipsoidal aggregate and FIG. 3b is a boundary transition zone for a convex polyhedral aggregate;
FIGS. 4 a-4 b are schematic diagrams of mesh division of the inside of different aggregates, wherein FIG. 4a is an ellipsoidal aggregate and FIG. 4b is a convex polyhedral aggregate;
5 a-5 c are damage evolution processes and failure modes of different sections when simulation tests are performed on concrete samples;
fig. 6 a-6 b are an overall fracture diagram and a fracture form diagram of a concrete sample at the end of model loading, wherein fig. 6a is the overall fracture diagram and fig. 6b is the fracture form.
Detailed Description
The present invention will now be described in further detail with reference to the accompanying drawings. In the description of the present application, it is to be understood that the terms "left side", "right side", "upper part", "lower part", etc., indicate orientations or positional relationships based on those shown in the drawings, and are only for convenience of describing the present invention and simplifying the description, but do not indicate or imply that the referred device or element must have a specific orientation, be constructed in a specific orientation, and be operated, and that "first", "second", etc., do not represent an important degree of the component parts, and thus are not to be construed as limiting the present invention. The specific dimensions used in the present example are only for illustrating the technical solution and do not limit the scope of protection of the present invention.
As explained in the background art, in the present simulation test about the problem of concrete failure and damage, the interface transition region part is often ignored, so that a great risk exists in the accuracy of the test calculation result.
Therefore, the method for establishing the concrete three-dimensional multiphase mesoscopic model and simulating the numerical value is provided, the relation among the aggregate, the mortar and the interface transition area is fully considered by establishing the concrete three-dimensional multiphase mesoscopic model, particularly the non-uniformity of the interface transition area, and the damage evolution process of the concrete sample as a three-dimensional space structure can be clearly shown.
The method specifically comprises the following steps:
step S1: establishing a concrete three-dimensional random aggregate model, wherein the concrete three-dimensional random aggregate model comprises a three-dimensional spherical aggregate model, a three-dimensional ellipsoid aggregate model and a three-dimensional random convex polyhedron aggregate model; the method is characterized in that each model is established, a more accurate method is used for judging the separation between the aggregate and the boundary and between the aggregate, and compared with the conventional method that the distance between the centers of the ellipsoids is larger than the sum of two major and minor axes, the time required for judging the separation of the aggregate can be greatly reduced, and what needs to be explained is why only spherical, ellipsoidal (figure 1a) and convex polyhedral aggregate (figure 1b) models are established, so that various aggregate structures are strictly defined, but the general establishment of the aggregate models in the three forms can cover most of the situations and completely meet the requirements of test simulation;
the method comprises the following specific steps:
step S11: determining the number of the aggregates in each particle size range, and obtaining the percentage of the aggregates in each particle size range in the total volume of the aggregates by adopting a Fuller grading formula
Figure BDA0003476179310000061
In the formula (1), D0Is the diameter of the sieve hole, DmaxMaximum aggregate particle size, P, to pass through the screenc(D<D0) To pass through a diameter D0The aggregate cumulative volume percentage of the sieve pores is the percentage of the aggregate in the total volume in the particle size range;
substituting the percentage of the aggregate in the total volume in the obtained particle size range into a formula (2) to determine the number of the aggregates in each particle size range, wherein the formula (2) is
Figure BDA0003476179310000071
In the formula (2), DiThe aggregate in this particle size range represents the particle size, V is the total volume of the aggregate, PciThe volume of the aggregate accounts for the percentage of the total volume of the aggregate in the particle size range; at the time of the test, PciNamely the percentage of aggregate in the total volume within different particle size ranges obtained by a Fuller grading formula;
step S12: according to the Monte Carlo principle, randomly generating parameters of the aggregate in each particle size range, wherein the parameters comprise the position and the size parameters of the aggregate;
step S13: carrying out phase separation judgment on the aggregates by using the obtained aggregate parameters in each particle size range, namely carrying out phase separation judgment on spherical aggregates, ellipsoidal aggregates and random convex polyhedral aggregates, and compiling an aggregate random-generated phase separation judgment program by adopting a Python language;
the method mainly comprises a spherical aggregate effectiveness judgment method, a spatial ellipsoid quadratic matrix and an ellipsoid aggregate effectiveness judgment method; the effectiveness judgment method of the spherical aggregate comprises the following steps: provided with a spherical aggregate Ai(xci,yci,zci) Spherical aggregate A0(xc0,yc0,zc0) Spherical aggregate AiSpherical aggregate A0Respectively has a radius of ri、r0Then the judgment equation is
Figure BDA0003476179310000072
Then, let the coordinates of the left lower corner point and the right upper corner point of the bounding cuboid be (x)L,yL,zL) And (x)U,yU,zU) The spherical center of each spherical aggregate is AiThe coordinates of the sphere center are (x)ci,yci,zci) Radius riThen spherical aggregate AiThe decision equation for separation from the boundary is:
Figure BDA0003476179310000073
spherical aggregate A0Is spherical aggregate AiBased on the random convex polyhedral aggregate A generated by adopting an inscription method0Each vertex position of the spherical aggregate A is random and is connected with the spherical aggregate AiOn the sphere, the coordinates of each vertex of the random convex polyhedron are expressed as
Figure BDA0003476179310000074
In the formula (4), the spherical aggregate A0Has a spherical center coordinate of (x)c0,yc0,zc0) Radius r0Let the coordinates start on the y-axis and be positive clockwise, αiIs an angle offset from the z-axis, positive in the clockwise direction, βiThe angle of rotation around the center of the sphere in the xOy plane;
then, similarly, let the coordinates of the left lower corner point and the right upper corner point of the bounding cuboid be (x) respectivelyL,yL,zL) And (x)U,yU,zU) Then random convex polyhedral aggregate A0The decision equation for separation from the boundary is:
Figure BDA0003476179310000081
the validity judgment method of the ellipsoid aggregate comprises the following steps: let the quadratic forms of ellipsoid A and ellipsoid B be X respectivelyTAX is 0 and XTBX is 0, then the generalized characteristic polynomials of ellipsoid a and ellipsoid B are
f(λ)＝det(λA+B)，
If the equation f (λ) is 0, there are two different positive roots, then ellipsoid a is separated from ellipsoid B; ellipsoid A intersects ellipsoid B in other cases;
then, the method for determining the separation of the ellipsoidal aggregate from the boundary is as follows: the equations of the ellipsoid and the plane are combined to obtain a matrix equation
Figure BDA0003476179310000082
In the formula (6), the reaction mixture is,
Figure BDA0003476179310000083
is a three-order symmetrical square matrix,
order matrix
Figure BDA0003476179310000084
If matrices A and B satisfy the condition | A +>0 and (a)11+a22)|B|<0, the ellipsoid is intersected with the plane, otherwise, the ellipsoid is separated from the plane;
writing a random generation program of spherical aggregate, ellipsoidal aggregate and convex polyhedral aggregate by adopting Python language;
step S14: and embedding the Python program of the judgment result into ABAQUS to generate a three-dimensional random aggregate geometric model.
Step S2: defining aggregate units based on the concrete three-dimensional random aggregate model established in the step S1, defining mortar units according to the size of the concrete test piece, and establishing a non-uniform concrete three-dimensional multi-phase mesoscopic model in the interface transition region;
the specific steps for establishing the three-dimensional multiphase mesoscopic model are as follows:
step S21: if a three-dimensional multiphase mesoscopic model is to be established, defining a tension-plasticity damage constitutive relation and determining material parameters, wherein the tension-plasticity damage constitutive relation is expressed by the following formula
Figure BDA0003476179310000085
In formula (7), σtuIs the peak stress of the material, GfTo fracture energy, uckIs a cracking displacement; in the established three-dimensional multi-phase microscopic modelIn the model, the constitutive relation and the damage evolution equation of the softening section are respectively the peak stress and the fracture energy G of the materialfAnd crack displacement uckControl of where σtuAnd GfAll the material constants are the material constants of the concrete test piece and can be measured through tests, so that the stress value and the damage variable are the cracking displacement uckThe stress change of the damage unit is not related to the unit size in actual calculation, so that the grid sensitivity of the model is greatly reduced;
step S22: establishing a three-dimensional multi-phase mesoscopic concrete model with non-uniformity in an interface transition region, wherein the thickness and the strength of the interface transition region are changed along with the change of the particle size of the aggregate, the thickness and the strength of the interface transition region are in a linear proportional relation with the particle size of the aggregate, and the strength of the interface transition region and the thickness of the interface transition region are in an exponential function relation, and the non-uniformity of the interface transition region is considered, namely the thickness and the strength of the interface transition region outside each aggregate are changed along with the change of the particle size of the aggregate, so that the mechanical characteristics of the interface transition region are truly reflected; wherein the relationship between the strength of the interface transition region and the thickness of the interface transition region is
ξ＝ebδ-c+d (8)
In the formula (8), xi is the ratio of the strength of the interface transition area to the strength of the mortar, delta is the thickness of the interface transition area, c and d are parameters of an exponential function, and the two-point coordinate (delta)min,ξmax) And (delta)max,ξmin) Substituting the expression to obtain;
step S23: determining material parameters of the concrete test piece based on the formula (8), substituting the determined mortar strength, the strength of the interface transition zone and the fracture energy into the formula (7), determining the plastic damage parameters of the mortar and the interface transition zone, and generating sigma by using Python script programmingt-uckAnd dt-uckA table function;
step S24: the interface transition zone is wrapped in thickness outside the aggregate and is completed by cutting and merging operations of Assembly modules in ABAQUS.
Step S3: setting an inner grid transition surface and an outer grid transition surface for the non-uniform concrete three-dimensional multi-phase mesoscopic model in the interface transition area; the method is characterized in that high-density (small-grid) grids are arranged in an area (namely an interface transition area) of key research, the size of seeds is equivalent to the thickness of the grids, sparse (large-grid) grids are arranged in an aggregate unit and a mortar unit, and the unit size of the interface transition area is small, so that grid transition surfaces are arranged at the junctions of the interface transition area and the aggregate unit and the mortar unit respectively, the high-density grids in the interface transition area are in smooth transition to the sparse grids of the aggregate unit and the mortar unit, the mesoscopic characteristic of a three-dimensional model can be fully embodied, the total amount of the units is effectively reduced, and the calculation efficiency of the three-dimensional multiphase mesoscopic model is improved;
the method for establishing the mesh transition surface comprises the steps of respectively establishing a concentric surface which is concentric with the centroid of the aggregate and has different grain sizes in the aggregate unit on the inner side of the interface transition area and the mortar unit on the outer side of the interface transition area, programming the establishing process by adopting a Python script, and embedding the building into ABAQUS to finish the automatic generation of the inner and outer mesh transition surfaces.
Step S4: based on the model obtained in the step S3, carrying out numerical simulation on the three-dimensional failure and damage process of the concrete test piece by using a displacement loading method;
step S41: applying boundary conditions to the non-uniform concrete three-dimensional multi-phase mesoscopic model of the interface transition area to be tested, and applying displacement load at a loading point;
step S42: setting a damage threshold, judging that the unit fails and breaks when the tensile damage value reaches the damage threshold, wherein the larger the damage value is, the more serious the material failure and the damage is, and taking the damage threshold as 0.9, namely, when the tensile damage value reaches the damage threshold, the unit fails and breaks; during uniaxial tension, analyzing the damage evolution process and the failure damage form of a plurality of sections of the concrete sample, wherein the method can analyze the three-dimensional failure damage process of the concrete sample from a plurality of microscopic sections, and then comparing a damage cloud picture of an internal interface transition area of the concrete sample with a macroscopic damage cloud picture of the outer side of the concrete sample to more clearly show the damage evolution process of the concrete sample as a three-dimensional space structure;
step S43: and storing the obtained damage value in a result information matrix, establishing and solving a model in ABAQUS, and processing elements in the result information matrix after calculation to finish the three-dimensional damage evolution process and the fracture form of the simulated concrete test piece.
In order to verify the accuracy of the model provided by the application, the application performs a specific embodiment, and in the embodiment, the determination is performed based on a Fuller grading formula, and the aggregate particle size range is 5mm to 20mm, so that the aggregate with the particle size range of 15mm to 20mm accounts for 13.4% of the total volume of the aggregate, the aggregate with the particle size range of 10mm to 15mm accounts for 15.9% of the total volume of the aggregate, and the aggregate with the particle size range of 5mm to 10mm accounts for 20.7% of the total volume of the aggregate. In order to ensure the smooth feeding of the aggregate with large particle size, the aggregate parameters are randomly generated according to the order of the particle size range of the aggregate from large to small.
The number of the aggregates in each particle size range is determined by the formula (2), 24 aggregates with the particle size of 15mm-20mm are thrown in the cubic test piece with the size of 100mm × 100mm × 100mm, 78 aggregates with the particle size of 10mm-15mm are thrown in the cubic test piece, and 469 aggregates with the particle size of 5mm-10mm are thrown in the cubic test piece.
Then, randomly generating all parameters of the aggregate according to a Monte Carlo principle, wherein the parameters mainly comprise a position parameter (namely an aggregate central coordinate) and a size parameter (namely an aggregate particle size) of the aggregate; then, carrying out phase separation judgment on the aggregate, wherein as explained above, the aggregate form mainly comprises spherical aggregate, ellipsoidal aggregate and convex polyhedral aggregate, and mainly comprises an effectiveness judgment method of the spherical aggregate, a quadratic matrix of a space ellipsoid, an effectiveness judgment method of the ellipsoidal aggregate and the like, a phase separation judgment program randomly generated by the aggregate is written by adopting Python language, in the embodiment, a generalized characteristic value of a characteristic equation is solved by utilizing a linear.eig () function in a SciPy module of the Python language, because the linear.eig () function defines a generalized characteristic polynomial as f (lambda) det (lambda A-B) when solving the generalized characteristic value, in the embodiment, a minus sign is added in front of the matrix A, the generalized characteristic equation actually judged by the program becomes f (lambda) det (-lambda A-B) 0, and two sides of the equation are multiplied by-1 to obtain det (lambda A + B) 0, the generalized eigenvalue obtained at this time is the solution.
The relationship curve of the obtained ratio xi and the thickness delta of the interface transition zone of the non-uniform concrete three-dimensional multi-phase mesoscopic model of the interface transition zone established in the embodiment is shown in figure 2; when the material parameters are determined, trial calculation is carried out, wherein b is-7.5 in formula (8), the elastic modulus of the interface transition region is 60% -80% of the mortar matrix, the strength is 35% -65% of the mortar matrix, the fracture energy is 40% -90% of the mortar matrix, and the mechanical parameters of each phase of concrete are shown in the following table 1;
TABLE 1 mechanics parameter table of concrete phases
Figure BDA0003476179310000111
Substituting the tensile strength, the fracture energy and other material parameters of the mortar and the interface transition zone into a formula (7) according to the table 1 to complete the determination of the plastic damage parameters of the mortar and the Interface Transition Zone (ITZ), and generating sigma by using Python script programmingt-uckAnd dt-uckA table function; the interface transition region is wrapped outside the aggregate in an equal-thickness mode, cutting (Cut) and merging (Merge) operations of an Assembly module in ABAQUS are adopted to complete the whole process, Python language programming is used for achieving the whole process, and in order to better show the shape of the interface transition region, schematic diagrams of the interface transition region of the ellipsoid aggregate and the convex polyhedron aggregate are shown in figures 3 a-3 b.
In order to effectively reduce the number of units, a grid transition surface is required to be arranged in each of the interface transition area and the boundary area of the aggregate and the external mortar in the interface transition area, so that natural and smooth transition from the small-size grid of the interface transition area to the large-size grid of the aggregate and the mortar is realized, and the purpose of the method is to further improve the accuracy of test simulation, and the grid subdivision diagrams in the ellipsoidal aggregate and the convex polyhedral aggregate are shown in fig. 4 a-4 b.
Next, a displacement loading method is adopted to simulate the three-dimensional failure damage process of the concrete sample, and the following simulation process is provided in the embodiment:
firstly, applying corresponding boundary conditions to a researched concrete three-dimensional multiphase mesoscopic model, applying displacement load at a loading point, and applying uniform plane load on the right side boundary of a uniaxial tension test piece;
in the embodiment, the size of a concrete sample is 100mm multiplied by 100mm, the particle size of aggregate is 5mm-20mm, horizontal constraint is applied to the left end of the concrete sample, vertical constraint is applied to the middle line of the left end, displacement control loading is adopted, and uniform displacement load with the size of 0.25mm is applied to the right end of the concrete sample;
secondly, describing the failure damage form and damage fracture degree of the material by using a damage cloud chart at the end of ABAQUS calculation, representing the tensile damage value of the material by using DAMAGET, wherein the range of the DAMAGET is 0-1, the larger the damage value is, the more serious the material failure damage is, setting the damage threshold value to be 0.9, and when the tensile damage value reaches the damage threshold value, considering that the unit failure fracture damage occurs;
thirdly, analyzing the damage evolution process and the failure damage form of 30%, 60% and 90% sections (i, ii and iii sections, respectively) of the uniaxial tensile concrete specimen along the X direction, wherein the final damage cloud chart of each section of the ellipsoidal aggregate model in the embodiment is shown in fig. 5 a-5 c, which respectively represents the i, ii and iii sections;
fourth, the model is built and solved in ABAQUS to obtain the overall fracture map (fig. 6a) and fracture morphology (fig. 6b) at the end of the model loading. Because the numerical calculation is performed by using the plastic damage model, a plurality of displacement loading incremental steps are often performed in the calculation process, and in this embodiment, the loading displacement u is 0.25umax、u＝0.5umax、u＝0.75umaxAnd u ═ umaxAnd extracting the damage condition of the structure in four loading steps to analyze the failure damage process in the structure, comparing the damage fracture condition of each section in the test piece with the macroscopic damage fracture condition outside the test piece, and obtaining a damage cloud chart of fig. 6b, wherein the unit of the cluster represents that the material is fractured and damaged, and the damage value of the unit in the model is changed between 0 and 1.
Therefore, the characteristics of the interface transition region are fully considered by utilizing the three-dimensional multiphase mesoscopic model established by the method, and the damage evolution process of the concrete as a three-dimensional space structure can be clearly shown.
It will be understood by those skilled in the art that, unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs. It will be further understood that terms, such as those defined in commonly used dictionaries, should be interpreted as having a meaning that is consistent with their meaning in the context of the prior art and will not be interpreted in an idealized or overly formal sense unless expressly so defined herein.
The meaning of "and/or" as used herein is intended to include both the individual components or both.
The term "connected" as used herein may mean either a direct connection between components or an indirect connection between components via other components.
In light of the foregoing description of the preferred embodiment of the present invention, many modifications and variations will be apparent to those skilled in the art without departing from the spirit and scope of the invention. The technical scope of the present invention is not limited to the content of the specification, and must be determined according to the scope of the claims.

Claims (8)

1. A method for building and simulating numerical values of a concrete three-dimensional multiphase mesoscopic model is characterized by comprising the following steps of: the method specifically comprises the following steps:
step S1: establishing a concrete three-dimensional random aggregate model, wherein the concrete three-dimensional random aggregate model comprises a three-dimensional spherical aggregate model, a three-dimensional ellipsoid aggregate model and a three-dimensional random convex polyhedron aggregate model;
step S2: defining aggregate units based on the concrete three-dimensional random aggregate model established in the step S1, defining mortar units according to the size of the concrete test piece, and establishing a non-uniform concrete three-dimensional multi-phase mesoscopic model in the interface transition region;
step S3: setting an inner grid transition surface and an outer grid transition surface for the non-uniform concrete three-dimensional multi-phase mesoscopic model in the interface transition area;
step S4: and based on the model obtained in the step S3, carrying out numerical simulation on the three-dimensional failure damage process of the concrete sample by using a displacement loading method.
2. The method for building and numerically simulating the three-dimensional multiphase mesoscopic concrete model according to claim 1, wherein the method comprises the following steps: in step S1, the step of building the concrete three-dimensional random aggregate model specifically includes:
step S11: determining the number of the aggregates in each particle size range, and obtaining the percentage of the aggregates in each particle size range in the total volume of the aggregates by adopting a Fuller grading formula
Figure FDA0003476179300000011
In the formula (1), D0Is the diameter of the sieve hole, DmaxMaximum aggregate particle size, P, to pass through the screenc(D<D0) To pass through a diameter D0The aggregate cumulative volume percentage of the sieve pores is the percentage of the aggregate in the total volume in the particle size range;
substituting the percentage of the aggregate in the total volume in the obtained particle size range into a formula (2) to determine the number of the aggregates in each particle size range, wherein the formula (2) is
Figure FDA0003476179300000012
In the formula (2), DiThe aggregate in this particle size range represents the particle size, V is the total volume of the aggregate, PciThe volume of the aggregate accounts for the total volume of the aggregate within the particle size range;
step S12: according to the Monte Carlo principle, randomly generating parameters of the aggregate in each particle size range, wherein the parameters comprise the position and the size parameters of the aggregate;
step S13: carrying out phase separation judgment on the aggregates by using the obtained aggregate parameters in each particle size range, namely carrying out phase separation judgment on spherical aggregates, ellipsoidal aggregates and random convex polyhedral aggregates;
step S14: and embedding the Python program of the judgment result into ABAQUS to generate a three-dimensional random aggregate geometric model.
3. The method for building and numerically simulating the three-dimensional multiphase mesoscopic concrete model according to claim 2, wherein the method comprises the following steps: in step S13, the phase separation determination of the aggregate mainly includes a spherical aggregate validity determination method, a quadratic matrix of a spatial ellipsoid, and an ellipsoid aggregate validity determination method;
the effectiveness judgment method of the spherical aggregate comprises the following steps: setting spherical aggregate Ai(xci,yci,zci) Spherical aggregate A0(xc0,yc0,zc0) Spherical aggregate AiSpherical aggregate A0Respectively has a radius of ri、r0Then the judgment equation is
Figure FDA0003476179300000021
Then, let the coordinates of the left lower corner point and the right upper corner point of the bounding cuboid be (x)L,yL,zL) And (x)U,yU,zU) The spherical center of each spherical aggregate is AiThe coordinates of the sphere center are (x)ci,yci,zci) Radius riThen spherical aggregate AiThe decision equation for separation from the boundary is:
Figure FDA0003476179300000022
spherical aggregate A0Is spherical aggregate AiBased on the random convex polyhedral aggregate A generated by adopting an inscription method0Each vertex position of the spherical aggregate A is random and is connected with the spherical aggregate A outside the spherical aggregate AiOn the sphere, the coordinates of each vertex of the random convex polyhedron are expressed as
Figure FDA0003476179300000023
In the formula (4), the spherical aggregate A0Has a sphere center coordinate of (x)c0,yc0,zc0) Radius r0Let the coordinates start on the y-axis and be positive clockwise, αiIs an angle offset from the z-axis, positive in the clockwise direction, βiThe angle of rotation around the center of the sphere in the xOy plane;
then, similarly, let the coordinates of the left lower corner point and the right upper corner point of the bounding cuboid be (x) respectivelyL,yL,zL) And (x)U,yU,zU) Then random convex polyhedral aggregate A0The decision equation for separation from the boundary is:
Figure FDA0003476179300000024
the validity judgment method of the ellipsoid aggregate comprises the following steps: let the quadratic forms of ellipsoid A and ellipsoid B be X respectivelyTAX is 0 and XTBX is 0, then the generalized characteristic polynomials of ellipsoid a and ellipsoid B are
f(λ)＝det(λA+B)，
If the equation f (λ) is 0, there are two different positive roots, then ellipsoid a is separated from ellipsoid B; ellipsoid A intersects ellipsoid B in other cases;
then, the method for determining the separation of the ellipsoidal aggregate from the boundary is as follows: the equations of the ellipsoid and the plane are combined to obtain a matrix equation
Figure FDA0003476179300000031
In the formula (6), the reaction mixture is,
Figure FDA0003476179300000032
is a three-order symmetrical square matrix,
order matrix
Figure FDA0003476179300000033
If the matrixes A and B satisfy the condition | A +>0 and (a)11+a22)|B|<0, the ellipsoid intersects the plane, otherwise, the ellipsoid is separated from the plane.
4. The method for building and numerically simulating the three-dimensional multiphase mesoscopic concrete model according to claim 3, wherein the method comprises the following steps: the specific steps of establishing the non-uniform concrete three-dimensional multiphase mesoscopic model in the interface transition area in the step S2 are as follows:
step S21: defining a tension plasticity damage constitutive relation and determining material parameters, wherein the tension plasticity damage constitutive relation formula is as follows
Figure FDA0003476179300000034
In formula (7), σtuIs the peak stress of the material, GfTo fracture energy, uckIs a cracking displacement;
step S22: establishing a three-dimensional multi-phase mesoscopic model of the non-uniform concrete in the interface transition region, wherein the three-dimensional multi-phase mesoscopic model comprises the linear proportional relation between the thickness of the interface transition region and the particle size of aggregate, and the exponential function relation between the strength of the interface transition region and the thickness of the interface transition region, and the relation between the strength of the interface transition region and the thickness of the interface transition region is
ξ＝ebδ-c+d (8)
In the formula (8), xi is the ratio of the strength of the interface transition area to the strength of the mortar, delta is the thickness of the interface transition area, c and d are parameters of an exponential function, and the two-point coordinate (delta)min,ξmax) And (delta)max,ξmin) Substituting the expression to obtain;
step S23: determining material parameters of the concrete test piece based on the formula (8), substituting the determined mortar strength, the strength of the interface transition zone and the fracture energy into the formula (7), determining the plastic damage parameters of the mortar and the interface transition zone, and generating sigma by using Python script programmingt-uckAnd dt-uckA table function;
step S24: the interface transition zone is wrapped in thickness outside the aggregate and is completed by cutting and merging operations of Assembly modules in ABAQUS.
5. The method for building and numerically simulating the three-dimensional multiphase mesoscopic concrete model according to claim 4, wherein the method comprises the following steps: in step S3, high-density grids are arranged in the interface transition area, the size of the seeds is equivalent to the thickness of the seeds, sparse grids are arranged in the aggregate units and the mortar units, and grid transition surfaces are arranged at the junctions of the interface transition area with the aggregate units and the mortar units, respectively, so that the high-density grids in the interface transition area are in smooth transition to the sparse grids of the aggregate units and the mortar units.
6. The method for building and numerically simulating the three-dimensional multiphase mesoscopic concrete model according to claim 5, wherein the method comprises the following steps: the method for establishing the grid transition surface comprises the steps of respectively establishing a concentric surface which is concentric with the centroid of the aggregate and has different grain sizes in the aggregate unit on the inner side of the interface transition area and the mortar unit on the outer side of the interface transition area.
7. The method for building and numerically simulating the three-dimensional multiphase mesoscopic concrete model according to claim 5, wherein the method comprises the following steps: the specific steps of step S4 are:
step S41: applying boundary conditions to the non-uniform concrete three-dimensional multi-phase mesoscopic model of the interface transition area to be tested, and applying displacement load at a loading point;
step S42: setting a damage threshold, judging that the unit fails and breaks when the tensile damage value reaches the damage threshold, wherein the larger the damage value is, the more serious the material failure and damage is, and the damage threshold is 0.9;
step S43: and storing the obtained damage value in a result information matrix, and processing elements in the result information matrix after calculation to finish the three-dimensional damage evolution process and the fracture form of the simulated concrete test piece.
8. The method for building and numerically simulating the three-dimensional multiphase mesoscopic concrete model according to claim 7, wherein the method comprises the following steps: when a concrete three-dimensional multiphase mesoscopic model is subjected to test simulation, after a damage threshold value is set, describing the failure damage form and damage fracture degree of a material by using a damage cloud chart at the end of ABAQUS calculation;
and simultaneously, when the load is applied to the side boundary of the uniaxial tension test piece for analysis, the damage evolution process and the failure damage form of a plurality of sections of the concrete test piece are analyzed.
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